%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:20:26 EDT 2022

% Result   : Theorem 0.18s 0.49s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   26 (   5 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   71 (  24   ~;  15   |;  18   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   54 (  43   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f40,plain,
    $false,
    inference(unit_resulting_resolution,[],[f30,f35,f36,f32]) ).

fof(f32,plain,
    ! [X3,X0,X1] :
      ( ~ member(X3,X0)
      | member(X1,sum(X0))
      | ~ member(X1,X3) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( ( member(X1,sK3(X0,X1))
          & member(sK3(X0,X1),X0) )
        | ~ member(X1,sum(X0)) )
      & ( member(X1,sum(X0))
        | ! [X3] :
            ( ~ member(X1,X3)
            | ~ member(X3,X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f25,f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X1,X2)
          & member(X2,X0) )
     => ( member(X1,sK3(X0,X1))
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( member(X1,X2)
            & member(X2,X0) )
        | ~ member(X1,sum(X0)) )
      & ( member(X1,sum(X0))
        | ! [X3] :
            ( ~ member(X1,X3)
            | ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( member(X1,X2)
            & member(X2,X0) )
        | ~ member(X1,sum(X0)) )
      & ( member(X1,sum(X0))
        | ! [X2] :
            ( ~ member(X1,X2)
            | ~ member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X1,X2)
          & member(X2,X0) )
    <=> member(X1,sum(X0)) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X2] :
      ( member(X2,sum(X0))
    <=> ? [X4] :
          ( member(X4,X0)
          & member(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).

fof(f36,plain,
    ~ member(sK0(sum(sK1),sK2),sum(sK1)),
    inference(unit_resulting_resolution,[],[f31,f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( ~ member(sK0(X0,X1),X0)
        & member(sK0(X0,X1),X1) )
      | subset(X1,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1) )
     => ( ~ member(sK0(X0,X1),X0)
        & member(sK0(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1) )
      | subset(X1,X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) )
     => subset(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).

fof(f31,plain,
    ~ subset(sK2,sum(sK1)),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ( ~ subset(sK2,sum(sK1))
    & member(sK2,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f18,f22]) ).

fof(f22,plain,
    ( ? [X0,X1] :
        ( ~ subset(X1,sum(X0))
        & member(X1,X0) )
   => ( ~ subset(sK2,sum(sK1))
      & member(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1] :
      ( ~ subset(X1,sum(X0))
      & member(X1,X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X1,X0] :
        ( member(X1,X0)
       => subset(X1,sum(X0)) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X2] :
        ( member(X2,X0)
       => subset(X2,sum(X0)) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0,X2] :
      ( member(X2,X0)
     => subset(X2,sum(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI43) ).

fof(f35,plain,
    member(sK0(sum(sK1),sK2),sK2),
    inference(unit_resulting_resolution,[],[f31,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f30,plain,
    member(sK2,sK1),
    inference(cnf_transformation,[],[f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.32  % Computer : n023.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Tue Aug 30 14:02:20 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.48  % (3999)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.48  % (3999)First to succeed.
% 0.18/0.49  % (4016)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.18/0.49  % (3992)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.49  % (3999)Refutation found. Thanks to Tanya!
% 0.18/0.49  % SZS status Theorem for theBenchmark
% 0.18/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49  % (3999)------------------------------
% 0.18/0.49  % (3999)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (3999)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49  % (3999)Termination reason: Refutation
% 0.18/0.49  
% 0.18/0.49  % (3999)Memory used [KB]: 5884
% 0.18/0.49  % (3999)Time elapsed: 0.094 s
% 0.18/0.49  % (3999)Instructions burned: 2 (million)
% 0.18/0.49  % (3999)------------------------------
% 0.18/0.49  % (3999)------------------------------
% 0.18/0.49  % (3987)Success in time 0.159 s
%------------------------------------------------------------------------------